Simplified synthesis of spiro‐bridged ladder‐type poly(p‐phenylene)

In this study, a simplified route to synthesize soluble, spiro‐bridged ladder‐type poly(p‐phenylene)s (spiro‐LPPP) was developed. The new, simplified synthesis route for spiro‐LPPP involves two reaction steps: a single‐stranded precursor polymer containing diaryloylbenzene building blocks was obtained by the Suzuki reaction, followed by a subsequent twofold cyclization cascade using methanesulfonic acid to form the target spiro‐LPPP. Spiro‐LPPP shows a well‐defined chemical structure, high molecular weight (M_n of 17,500 g/mol with a polydispersity index of 2.0), excellent thermal stability (5% weight loss at 370 °C), and good solubility in common organic solvents. Spiro‐LPPP emits blue light (λ_max,em = 455 nm) with the high solution PL quantum yield (94%). The spectral properties of spiro‐LPPP in the solid state are very similar to the solution properties, thus indicating a low degree of intermolecular aggregation. After annealing a thin film of spiro‐LPPP to 120 °C in air for 3 to 24 h, its emission spectrum is unchanged, reflecting excellent thermooxidative stability. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5137–5143, 2009     

Theorie der Flächenelemente höherer Ordnung des Raums von 3 Dimensionen

Ohne Zusammenfassung     

Harn

Ohne Zusammenfassung     

Hydrate frameworks involving the pyridazino[4,5‐d]pyridazine unit as a multiple hydrogen‐bond acceptor

1,4,5,8‐Tetramethylpyridazino[4,5‐d]pyridazine trihydrate, C₁₀H₁₂N₄·3H₂O, (I), and 1,2,3,6,7,8‐hexahydrocinnolino[5,4,3‐cde]cinnoline tetrahydrate, C₁₂H₁₂N₄·4H₂O, (II), exhibit exceptional functionality of the condensed N₄‐heteroaromatic frame as a symmetric acceptor of four hydrogen bonds [N...O = 2.843 (2)–2.8716 (10) Å]. Thus, all the N atoms of the electron‐deficient and highly π‐acidic polynitrogen heterocycles function as lone‐pair donors. In (I), all the molecular components lie on or across special positions; the site symmetry is 2/m for the organic and m2m and m for the two water molecules. In (II), the organic polycycle lies across a crystallographic inversion center. Both structures involve a hydrogen‐bonded centrosymmetric water–pyridazine dimer as the basic supramolecular unit, which is integrated into two‐dimensional [in (I)] and three‐dimensional [in (II)] hydrate frameworks by hydrogen bonding with the additional water molecules [O...O = 2.744 (2)–2.8827 (19) Å]. The hydrate connectivity exists in the form of an (H₂O)₃ trimer in (I) and as a one‐dimensional zigzag (H₂O)_n chain in (II).     

Ueber die Verf?lschungen des Bienenwachses und deren Erkennung

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A note on the multiplicity in factor ring

Let (R,m) = k[x ₁,..., x _n ](x ₁,...,x _n ) be a local polynomial ring (k being an algebraically closed field), and Q:= (F ₁,..., F _r )R be a primary ideal in R with respect to a maximal ideal m ⊂ R. In this short note we give a formula for the multiplicity e ₀ (QR/(F ₁)R, R/(F ₁)R). The author was supported by the grant No. 1/0262/03) of the Slovak Ministry of Education.     

Riemannian Submersions from Quaternionic Manifolds

In this paper we define the concept of quaternionic submersion, we study its fundamental properties and give an example.      

Fluid flow through a helical pipe

In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.